This invention relates to apparatus for reproducing four separate channels of information after recording or transmission on a medium having only two tracks, and presenting it on four loudspeakers to give the listener the illusion of sound coming from a corresponding number of separate sources. In particular it refers to the directional enhancement system described in co-pending application No. 13047/74 and is intended to form part of the processing apparatus of such a system.
In the processing apparatus of the directional enhancement system, control signals produced by the direction detection apparatus are processed by imposing suitable level-limiting and attack-decay characteristics upon them, prior to generating the coefficients of a modifying matrix for presentation to the matrix multiplier of the system. When more than one such control signal occurs simultaneously, it is the purpose of the present invention to alter the level-limiting characteristics dynamically in such a way that optimum placement and separation of the corresponding sound sources is achieved. This also ensures more accurate placement and better separation for single sources in intermediate directions between those for which control signals are provided.
The invention provides method and apparatus for the processing of simultaneously present control signals arising in a directional enhancement system so as to obtain optimum placement and separation characteristics for the corresponding sound sources when reproduced on the output devices, particularly with reference to the application of directional enhancement systems to quadraphonic sound systems.
The apparatus forms part of the processor of the directional enhancement system disclosed in co-pending application No. 13047/74 and is characterised by means for limiting all such signals present to a level which depends on the number and strengths of such signals. It may also be combined with a limit-type manual dimension control.
According to one aspect the invention provides, an apparatus for enhancing the directional content of information contained in a plurality of composite signals emanating from decoding apparatus, an automatic control system comprising; a summing device having a number of inputs equal to the number of control signals provided in said directional enhancement system and an output, and operative to provide at its output a signal equal to the sum of the signals presented at its input; a plurality of dividing devices each having a first input, a second input and an output, and operative to provide at its output the quotient of the division of the first signal presented to its first input by the second signal presented to its second input, one such dividing device being provided for each of the control signals, a different one of the control signals being applied to the first input of each dividing device, and the sum signal present at the output of the summing device being applied to the second input of each dividing device; a plurality of limiting devices, each having an input, and a control terminal, and operative to prevent the signal level at its input from rising above the level at its control terminal, one such limiting device being provided for each control signal, a different one of the output signals from the dividing devices being applied to the control terminal of each limiting device, and the input of the limiting device being connected to the control signal which is also applied to the first input of the dividing device whose output is applied to the control terminal of the limiting device; the whole system being operative to limit the sum of the control signals applied to its inputs to unity, while leaving unchanged the ratios between said control signals.
In the description of the Directional Enhancement System in the co-pending application No. 13047/74 it was stated that the effect of the system was to generate the coefficients of a modifying matrix M in accordance with predetermined equations and dependent on the direction of the predominant sound source as determined by the detector apparatus of the system, and to multiply the input decoded signals vector d by this matrix M to produce the modified decoded signals vector m, thereby altering the overall transmission matrix T.sub.o so that the predominant source appears only in the corresponding loudspeaker or loudspeakers, and furthermore maintaining constant total power from the speakers for every sound source present. The process is described by the equations ##EQU1## where T is the 4.times.4 transformation matrix from the original signals vector s to the modified decoded signals vector m, and EQU T=MT.sub.o ( 3)
where T.sub.o is the overall transformation matrix from the original signals vector s to the decoded signals vector d presented to the input of the Directional Enhancement System. The modifying matrix can be separated into two components, EQU M=B+I (4)
where I is the identity transformation and B represents the time-varying difference between M and I which is necessary to perform the required modification. If control signals c.sub..theta. are provided for several different control directions .theta., the matrix B can be written as a linear combination of the corresponding predetermined matrices for each direction, B.sub..theta., and since the c.sub..theta. vary with time. ##EQU2## It was shown that if the control parameters c.sub..theta. are allowed to take intermediate values between 0 and 1 when a signal source occured between two directions for which control signals were provided, and that if the sum of the control signals was always equal to 1, the resulting modifying matrix was reasonably effective in suppressing the transferred signals and in preserving constant total power from the speakers; in particular it was shown that for a center left or center right signal complete separation and correct placement of the signal is achieved, although the total power is reduced by 1.8 dB. The effect of the invention herein described is to limit the sum of the control signals dynamically to a value close to 1, thereby achieving practically optimum separation for all single sources wherever they occur. The exact condition for complete separation of sources at any direction has been determined and is given below.
In the case of an application to the SQ quadraphonic sound system of C.B.S. Inc., a directional enhancement system was described in which six control parameters were provided and six directional modifying matrices were implemented. The direction angles .theta. for which control signals and modifying matrices were provided were 0.degree. or center front, 45.degree. or right front, 135.degree. or right back, 180.degree. or center back, 225.degree. or left back and 315.degree. or left front. The modifying matrices were designated by the subscript corresponding to the direction angle .theta., and the coefficients of the corresponding B matrices were given as ##EQU3##
In order to evaluate the required combinations of these matrices to produce complete separation of sources placed elsewhere than at the corners and center front and center back positions, it will be necessary to see how these sources are encoded and decoded in the SQ system. Sources in the front and back quadrants are encoded directly according to the SQ matrix equations, but with sine and cosine functions usually provided by sine-cosine panning potentiometers. In the side quadrants these potentiometers do not provide the optimum encoding format and accordingly a position encoder has been used, which has the effect of providing signals to all four encoder inputs in accordance with equations given below. Thus, for signals between direction angles 0.degree. and 45.degree. the original signals vector takes the form ##EQU4## between 45.degree. and 135.degree. the vector takes the form ##EQU5## and for other directions symmetry relations exist which determine similar formats for the source signals vector. It is therefore only necessary to consider the appropriate values of the control coefficients to give complete separation of the signals in the formats given above, and to ensure that the symmetry of the system is correct, to obtain complete separation for any source position around the listener.
Consider now the requirements to be placed upon these coefficients. In the case of direction angles between 0.degree. and 45.degree. it is required that the only non-zero control parameters are c.sub.0 and c.sub.45, and that these should take values which are functions of the direction angle. To simplify the working, let EQU c.sub.0 =f(.theta.) (14)
and EQU c.sub.45 =g(.theta.) (15)
Then the modifying matrix M(.theta.) is given by EQU M(.theta.)=f(.theta.)B.sub.0 +g(.theta.)B.sub.45 +I (15)
The decoded signals vector is given by applying the transformation matrix T.sub.o to the source signals vector s, and writing EQU a=45.degree.-.theta. (16)
by the trigonometric identity cos x=sin (90.degree.-x) the source signals vector becomes ##EQU6## and the decoded signals vector is ##EQU7## Then the modified signals vector is given by EQU m=Md (1)
where ##EQU8## and the requirement for cancellation of the signals in the rear channels means that the bottom two rows of M must form a product with d of zero. This is true of both the real and imaginary parts of these products separately, and at first sight it looks as if there would be four equations to determine two unknowns; however, two of the equations turn out to be equivalent to the other two, which leads to the two distinct equations: ##EQU9## where t=tan a Eliminating g between these leads to ##EQU10## and eliminating f between them leads to ##EQU11## The real and imaginary components of the two front channels of the modified signals can then be found for each direction angle, and the resulting power level calculated. Also, the placement can be found, since the reproduced signals appear only in the front two channels, and in a ratio EQU t'=tan a'=m.sub.1 /m.sub.2 ( 25)
where the reproduced direction angle .theta.' is given by EQU .theta.'=45.degree.-a' (26)
The placement error is defined as the difference between the original direction angle and the reproduced direction angle, and as will be seen from Table 1, the maximum placement error in this range of source angles is 1.36.degree.. Such an error would be barely noticeable in a direct comparison between the original signals and the reproduced signals.
The total quadraphonic separation can be defined as the ratio of the signal power in the two channels in which the signal is necessary to the correct reproduction of its direction to that in the remaining two channels, expressed in decibels. In the ideal decoding system, it would of course be infinite for all source directions at all times, but in practice this is impossible because of tolerances in components, detector performance and so on. The TQS for a simple matrix decoder calculated on the above basis is always 0 dB, hence the figure achieved in a practical decoder is a reliable indicator of the improvement achieved relative to a simple matrix decoder.
Similar reasoning to that given above for the source angle between 0.degree. and 45.degree. leads to the same equations for f and g in the ranges 135.degree. to 180.degree., 180.degree. to 225.degree. and 315.degree. to 360.degree., and the control parameters are related to these functions according to the equations below: ##EQU12##
In the side quadrants, the requirement for total separation is that the two components of the reproduced signals appearing on the opposite side are always zero. By similar reasoning to the above, using the source signals format given in equation (13), the values of the control signals required are given by ##EQU13## where t=tan a as before, and a is related to .theta. in the two ranges as given below: ##EQU14## An additional useful feature of the values of d and e is that their sum is always 1. Furthermore, the sum of the values of f and g is also approximately 1, and it is therefore possible by means of comparatively simple limiting circuitry to obtain roughly the correct characteristics for the sum of the control signals. Before describing the actual circuitry required to do this, mention should be made of Table 1, in which the equations for d, e, f and g were evaluated at 5.degree. intervals on a computer, and the resulting decoded signals were found, together with the placement, total quadraphonic separation and total effective power from the four channels. It can be seen from this table that the placement error is always less than 1.4.degree. in the front and rear quadrants, and always less than 2.25.degree. in the side quadrants, and the total power output varies by less than 0.25 dB in the front and rear quadrants and less than 1.9 dB in the side quadrants. Thus the overall performance of such a system is substantially perfect in these respects.
It has also been found in listening tests that the effect of this control system when more than one signal is present is to assist the correct placement of all such signals, because although the resulting control signals fall below their maximum possible values for much of the time, whenever two equal signals are present at opposite ends of the room the control circuitry then works in a manner which is preferential to neither, but still increases their separation relative to that obtained from a simple matrix decoder. This impression has been confirmed by a mathematical study of the resulting modifying matrices and their effects on sources in the principal directions for which control signals are provided. It also appears that increased separation results when three equal signals are present simultaneously. Because this system acts instantaneously, the ear is never aware that the separation of multiple sources is reduced, since whenever one source is sufficiently predominant over the others, its separation is increased to the maximum possible extent, depending on the tolerances in the components of the system.
TABLE 1 __________________________________________________________________________ COMPUTER EVALUATION OF THE CONTROL PARAMETERS Source Placement Total Total Angle Error Effective Quadraphonic Control .theta. .theta.' - .theta. Power Separation Parameters deg. deg. dB dB .degree. 0 .degree. 45 .degree. 135 Sum __________________________________________________________________________ 0 0.00 0.00 99.99 1.0000 0.0000 0.0000 1.0000 5 -0.53 -0.07 99.99 0.9149 0.1799 0.0000 1.0947 10 -0.04 -0.13 99.99 0.8245 0.3346 0.0000 1.1591 15 -1.22 -0.18 81.10 0.7290 0.4693 0.0000 1.1983 20 -1.36 -0.21 78.06 0.6281 0.5876 0.0000 1.2157 25 -1.35 -0.23 76.28 0.5210 0.6923 0.0000 1.2133 30 -1.19 -0.23 76.28 0.4065 0.7850 0.0000 1.1915 35 -0.89 -0.19 74.10 0.2830 0.8670 0.0000 1.0872 40 -0.49 -0.12 72.13 0.1404 0.9387 0.0000 1.0872 45 0.00 0.00 70.86 0.0000 0.9394 0.0606 1.0000 50 -0.93 -0.31 70.96 0.0000 0.99394 0.0606 1.0000 55 -1.62 -0.62 71.12 0.0000 0.8806 0.1194 1.0000 60 -2.04 -0.90 71.92 0.0000 0.8234 0.1766 1.0000 65 - 2.21 -1.16 72.33 0.0000 0.7676 0.2324 1.0000 70 -2.12 -1.39 72.90 0.0000 0.7128 0.2872 1.0000 75 -1.81 -1.58 73.68 0.0000 0.6539 0.3411 1.0000 80 -1.34 -1.72 73.54 0.0000 0.6056 0.3944 1.0000 90 0.00 -1.84 73.42 0.0000 0.5000 0.5000 1.0000 __________________________________________________________________________
The data presented in Table 1 refers only to the first quadrant of the source direction angle, but the remaining quadrants have symmetry relations as given above, and the given data is sufficient to show the effects of the system in all four quadrants. In particular, the total quadraphonic separation only falls from infinity because of rounding inaccuracies in the precise values of the coefficients of equations (23), (24), (28) and (29) fed to the computer, and but for these would be infinite in all directions. However, as has been mentioned, no practical system could be expected to show separation much in excess of 40 dB, due to manufacturing tolerances not only in the system but also in the hardware which provides the input signals to the system.